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Let us imagine two worlds with the same number of people. In one world there is slightly more happiness than in the other. In the first world (the one with slightly less happiness) happiness is distributed more or less evenly. In the second world (with slightly more happiness), it is distributed in a wildly unequal way. Some people are extremely happy while many others are miserable. Utilitarianism must prefer the second world over the first. If we are in the world creating business, and we are limited to these two worlds, then utilitarianism actually requires us to create the second world.

I think there is something wrong here. This seems like a very counter-intuitive moral requirement. Few people would find it morally acceptable.

It seems to me that this argument shows that utilitarianism by itself cannot supply us with a complete moral code. At the very least, it needs to be supplemented by a principle governing distribution -- or replaced by a different principle.

Let me throw out one more idea. Classical utilitarians spoke of the "greatest good of the greatest number." Maybe we would be better off if we replaced that notion by some notion of the common good. And that would be something different from the good of the majority or of the greatest number. 

When we talk about the common good, we are talking about something that involves the good of every single person. If we pursue the common good, the no one is left behind. Everyone benefits. That's the whole point.